A2 Final Exam Review 22-23 S1 (Pt. 3)

Algebra 2 CP Final Exam Review, Pt. 3

Topic: Exponential Functions, Parent Functions, Polynomials

This assignment counts as a minor grade. Please complete it twice if your first grade is unsatisfactory.

Exponential functions have a variable as an exponent

Multiple Choice

Which of the following is an exponential function?

• $$f\left(x\right)=x^2$$

• $$f\left(x\right)=3x^3$$

• $$y=x^3$$

• $$f\left(x\right)=3^x$$

Exponential Growth vs Decay

Aysmptote of the Exponential parent function

The asymptote of the exponential parent function is the horizontal line y = 0.

Examples of exponential functions and their asymptotes

Multiple Choice

• y = 0

• y = 5

• y = 1

• All real numbers

Multiple Choice

• y = 2

• y = 0

• y = 6

• all real numbers

Domain and Range of a function

• Domain: the set of all possible inputs (x's)

• The domain of all exponential functions is "All real numbers."

• Range: the set of all possible outputs (y's)

• The range of an exponential function is limited by the function equation.

The asymptote of an exponential function is used to determine the range of that function.

The range of an exponential function can be written as y > asymptote.

Multiple Choice

What is the range of the following function?

$$y\ =\ 3^x\ -\ 2$$  

• $$y>2$$

• $$y\ge2$$

• $$y>-2$$

• $$y\ge-2$$

Multiple Choice

What is the range of the function?

• All real numbers

• y > 3

• y < 4

• Impossible to determine from the graph.

End Value When (b) > 1 (exponential growth )

Multiple Choice

Name the parent function. 

• constant

• square root

• linear

• absolute value

Multiple Choice

Name the parent function. 

• constant

• quadratic

• linear

• exponential

Multiple Choice

Which parent function matches the graph? 

• f(x) = x

• f(x) = x²

• f(x) =√(x)

• f(x) =∛(x)

Multiple Choice

Which parent function matches the graph?

• f(x) = x

• f(x)= x²

• f(x) = |x|

• f(x) = ab^x

Multiple Choice

What type of function is shown?

• linear

• quadratic

• square root

• absolute value

Multiple Choice

What type of function is shown?

• absolute value

• quadratic

• linear

• exponential

Multiple Choice

Which parent function matches the graph?

• y = |x|

• y = ∛(x)

• y = x²

• y = a⋅b^x

Match

Match the following

linear

absolute

quadratic

cubic

• linear

• absolute

• quadratic

• cubic

Multiple Choice

Name the parent function.

• linear

• quadratic

• cube root

• cubic

​The x-coordinates represent the DOMAIN

The y-coordinates represent the RANGE

Here are some different ways to represent domain and range.

X - Independent

• The X value is the independent value.  

• This is the category that influences the other.

• Example: any category with time like minutes, hours, days, weeks, …. is independent

Y - Dependent

• The Y value is the dependent value.  

• This is the value that is being changed Make the statement Y depends upon X

• Careful, the Y comes first in this statement.

Multiple Choice

Domain is: 

• All x values, from left to right.

• All y values, from bottom to top.

• All x values from bottom to top. 

• All y values from left to right.

Multiple Choice

Range is:

• All x values, from left to right.

• All y values, from bottom to top.

• All x values from bottom to top.

• All y values from left to right.

Multiple Choice

The name of all the possible inputs of a function:

• Domain

• Range

Multiple Choice

The name of all of the possible outputs of a function:

• Domain

• Range

Multiple Choice

How long you will need to wait in a line

• Dependent

• Independent

Multiple Choice

The number of people at a party.

• Dependent

• Independent

Multiple Choice

The amount of money you can earn at the bake sale.

• Dependent

• Independent

Multiple Choice

The number of people in line ahead of you.

• Dependent

• Independent

Multiple Choice

The number of hotel rooms needed for the band

• Dependent

• Independent

What is a Polynomial?

A polynomial is an expression involving a sum of powers in one or more variables multiplied by coefficients, where the powers must be whole.

What it IS and what it is NOT:

Positive vs Negative

• Functions with a POSITIVE leading coefficient - RIGHT end goes UP

• Functions with a NEGATIVE leading coefficient - RIGHT end goes DOWN

Multiple Select

Which graphs have a POSITIVE leading coefficient? (Check all that apply)

Odd vs Even

• Functions with an ODD degree - ends go in OPPOSITE directions

• Functions with an EVEN degree - ends go in the SAME direction

Multiple Select

Which graphs have an ODD degree? (Check all that apply)

Multiple Choice

$$\$$  Which could be the graph of  $$f\left(x\right)=2x^3+3x^2+4\ ?$$  

Multiple Choice

$$\$$ Which could be the graph of  $$f\left(x\right)=-3x^8+17x^6-14x^3+2x^2-1\ ?$$   

Factors & Zeros

If in factored form a polynomial

f(x) = (x-a)(x-b)(x-c), then

(x-a), (x-b), and (x-c) are "factors" and

a, b, and c are zeros - they are the x-intercepts of the graph found at points (a,0), (b,0), and (c,0).

*The zeros are the opposite of what you see in the parenthesis!

Multiple Choice

$$\$$  Which graph depicts the function  $$f\left(x\right)=\left(x-6\right)\left(x-3\right)\left(x+8\right)?$$  

End Behavior (Graphs)

Multiple Choice

Express the END BEHAVIOR of the graph shown.

• $$x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty\$$

  $$x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$$

• $$x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$$ $$x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$$

• $$x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$$ $$x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$$

• $$x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$$ $$x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$$

End Behavior (Equations)

Multiple Choice

Express the END BEHAVIOR of the function:  $$f\left(x\right)=-12x^7-19x^3+22$$  

• $$x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty\$$

  $$x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$$

• $$x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$$ $$x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$$

• $$x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$$ $$x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$$

• $$x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$$ $$x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$$

Multiple Choice

Express the END BEHAVIOR of the function:  $$f\left(x\right)=7x^4+9x^3-21$$  

• $$x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty\$$

  $$x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$$

• $$x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$$ $$x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$$

• $$x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$$ $$x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$$

• $$x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$$ $$x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$$